To “throw a curveball” is to exploit the element of surprise. In the popular imagination, baseball ranks second only to poker as the great game of American deception. A pitcher mixes up his pitches by unpredictably throwing fastballs, curveballs, sliders, and more exotic options. Though everyone appreciates that randomness is an important element of baseball, it’s not easy to say how successful players are in using it. Compared to tennis serves, baseball pitches are complicated.
About 60 percent of major-league pitches are fastballs, 13 percent are sliders, 12 percent are changeups, and 9 percent are curveballs. These are averages only. The likelihood of encountering a given pitch varies greatly according to the individual player, the number of outs, how close the score is, fatigue, injuries, the wind, and who knows what else.
Economists Kevin Kovash and Steven D. Levitt examined the randomness of pitching in a 2009 study using stats on 3 million major-league pitches from the 2002 to 2006 seasons. This paper, which also examined football, is a monument of sports scholarship. Their large dataset allowed them to demonstrate convincingly that real-world baseball and football choices are unrandom and outguessable.
They parceled their mountain of data into thousands of molehills wherein all the most obvious variables were the same. There would, for instance, be a number of cases where pitcher A had just thrown to batter B while the count was C and there had been D, E, F, and G pitches of the various types already thrown in the at-bat. If the pitcher had thrown a fastball this time, what were the chances his next pitch would be a fastball, too? That was the sort of question Kovash and Levitt asked.
They found that major-league pitchers overalternate, like everybody else. A pitcher who throws a fastball is about 4 percentage points less likely to throw one the next time. The tendency to switch varied with the type of pitch. A slider was about 2 percentage points less likely to be repeated. Because sliders are less common (about 13 percent of all pitches), that was the biggest alternation effect in relative terms. There was no overalternation found with changeups.
Is this news that players can use? There’s no doubt that it helps to know for certain what pitch is coming. Simply knowing that pitchers overalternate doesn’t tell you what’s coming next; it just shifts the probabilities around. Most of the time, the likeliest pitch will be a fastball.
Kovash and Levitt asked Major League Baseball executives to guesstimate how valuable it would be for a batter to know for certain that a fastball was coming, relative to a batter who expected otherwise and was surprised to get a fastball. (Are you still with me?) The estimated value was about .150 OPS (on-base plus slugging percentage). Among the stats-obsessed, it’s generally agreed that the OPS correlates with runs scored.
Kovash and Levitt then did a back-of-envelope calculation in which they assumed that batters could make use of even incremental shifts in probability and that the effect is linear. Knowing that a fastball is about 4 percentage points less likely to follow another fastball should be worth about 0.006 OPS. Over a season, each additional .001 of OPS is estimated to be worth about 2.16 extra runs. A team whose players were able to take full advantage of the unrandomness could gain ten to fifteen extra runs a year. Any manager would love that.
The question is whether batters can use those small shifts in probability. My hunch is that alert batters have a likely pitch in mind. I would imagine that they find it difficult to think of two pitches simultaneously, though, much less to prepare their muscles for them. In that case, the excess alternation effect would be useful only when it changes the “most likely pitch.” Most of the time it won’t, because of the simple fact that a fastball is almost five times more common than any other pitch. Kovash and Levitt’s linear estimate probably sets an upper limit on the potential advantage.
One safe bet is that the quality of randomizing in company softball games and Little League leaves something to be desired. When you are up at bat, here’s a way to take advantage of it, without any math.
Before every pitch, try to decide what pitch is most likely. You’re on your own there. Factor in everything you know except the psychology of randomness. When it’s a toss-up which pitch is most likely, favor the one that wasn’t just pitched.
Kovash and Levitt also examined statistics on every NFL play from 2001 through 2005. They found that NFL teams are worse randomizers than major-league pitchers. About 56 percent of football plays are passing, and 44 percent are running. A team that passed on the previous play was about 10 percentage points less likely to pass on the next play.
Teams were even more likely to switch after a play was unsuccessful. After a failed pass or run, the chance of a switch increased by 14.5 percentage points.
These huge differences ought to be exploitable. The economists compute that a team that uses this to anticipate plays could score about one extra point per game, or half a victory per sixteen-game season.
Once again, amateurs are likely to be worse randomizers. With only two common types of plays, not too different in frequency, outguessing stands a good chance of being advantageous.
• A pitcher who throws a fastball this time is several percentage points less likely to throw a fastball on the next pitch.
• In football, expect the opposite type of play (running or passing) next time, especially when the current play fizzled or was repeated twice in a row.